Existence of rational points as a homotopy limit problem

• Gereon Quick ^[1]
  1. [1] University of Münster

     University of Münster

     Kreisfreie Stadt Münster, Alemania

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 8 (August 2015), 2015, págs. 3466-3481
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.12.006
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• Resumen

  • We show that the existence of rational points on smooth varieties over a field can be detected using homotopy fixed points of étale topological types under the Galois action. As our main example we show that the surjectivity statement in Grothendieck's Section Conjecture would follow from the surjectivity of the map from fixed points to continuous homotopy fixed points on the level of connected components. Along the way we define a new model for the continuous étale homotopy fixed point space of a smooth variety over a field under the Galois action.